We emphasize that our asymptotic results also hold (and the convergence rate does not change) if we solve Newton systems exactly, and/or adopt deterministic stepsizes.
The covariance matrix for solving Newton systems exactly is \(\Xi ^\star = {\Omega ^\star }/(2+\beta /\tilde{\beta })\) .
However, it is not clear to us whether the same results hold when we approximately solve Newton systems via deterministic solvers, such as with CG and MINRES methods as employed in [1]}.
In that case, Lemma REF  does not hold and significant adjustments of the analysis are required.
